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Related papers: Bending of thin periodic plates

200 papers

The complete set of bounds for the technical constants of an elastic layer, plate or laminate is given. The bounds are valid in general, also for completely anisotropic bodies. They are obtained transforming the polar bounds previously…

Classical Physics · Physics 2023-11-15 Paolo Vannucci

Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…

Materials Science · Physics 2008-04-17 Francois Willot , Yves-Patrick Pellegrini , Pedro Ponte Castaneda

We prove the incompressible limit of non-isentropic inviscid elastodynamic equations with general initial data in 3D half-space. The deformation tensor is assumed to satisfy the neo-Hookean linear elasticity and degenerates in the normal…

Analysis of PDEs · Mathematics 2024-12-16 Jiawei Wang , Junyan Zhang

We consider a family of linearly elastic shells with thickness $2\varepsilon$ (where $\varepsilon$ is a small parameter). The shells are clamped along a portion of their lateral face, all having the same middle surface $S$, and may enter in…

Mathematical Physics · Physics 2016-11-23 Á. Rodríguez-Arós

We rigorously derive a Kirchhoff plate theory, via $\Gamma$-convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin sheet. The heterogeneity in the elastic properties of…

Analysis of PDEs · Mathematics 2018-07-17 Virginia Agostiniani , Alessandro Lucantonio , Danka Lučić

A new result enables direct calculation of thermoelastic damping in vibrating elastic solids. The mechanism for energy loss is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. The general result is combined…

Materials Science · Physics 2007-05-23 Andrew N. Norris , Douglas M. Photiadis

In the present article, we consider a thermoelastic plate of Reissner-Mindlin-Timoshenko type with the hyperbolic heat conduction arising from Cattaneo's law. In the absense of any additional mechanical dissipations, the system is often not…

Analysis of PDEs · Mathematics 2015-06-18 Michael Pokojovy

It has been claimed that quasistatic granular materials, as well as nanoscale materials, exhibit departures from elasticity even at small loadings. It is demonstrated, using 2D and 3D models with interparticle harmonic interactions, that…

Statistical Mechanics · Physics 2007-05-23 C. Goldenberg , I. Goldhirsch

Stationary whirling of slender and homogeneous (continuous) elastic shafts rotating around their axis, with pin-pin boundary condition at the ends, is revisited by considering the complete deformations in the cross section of the shaft. The…

Soft Condensed Matter · Physics 2020-03-18 S. Mora

In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous…

Analysis of PDEs · Mathematics 2021-06-22 Tadele Mengesha , James M. Scott

Among systems that display generic scale invariance, those whose asymptotic properties are anisotropic in space (strong anisotropy, SA) have received a relatively smaller attention, specially in the context of kinetic roughening for…

Statistical Mechanics · Physics 2015-06-11 Edoardo Vivo , Matteo Nicoli , Rodolfo Cuerno

This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are…

Numerical Analysis · Mathematics 2020-03-04 Peter Hornung , Martin Rumpf , Stefan Simon

We derive a general theory of effective properties in metasolids based on phononic crystals with low frequency resonances. We demonstrate that in general these structures need to be described by means of a frequency-dependent and non-local…

Materials Science · Physics 2015-12-09 Daniel Torrent , Yan Pennec , Bahram Djafari-Rouhani

The elastic energy of a bending-resistant interface depends both on its geometry and its material composition. We consider such a heterogeneous interface in the plane, modeled by a curve equipped with an additional density function. The…

Analysis of PDEs · Mathematics 2024-07-02 Anna Dall'Acqua , Gaspard Jankowiak , Leonie Langer , Fabian Rupp

In our analysis, we show that Baldelli and Bourdin's work is only valid when describing the behaviour of a film bonded to an elastic pseudo-foundation, where Poisson's ratios of both bodies are in between -1 and 0 or in between 0 and 0.5…

Soft Condensed Matter · Physics 2021-01-26 Kavinda Jayawardana

We report experimental results on the decay of wave turbulence in an elastic plate obtained by stopping the forcing from a stationary turbulent state. In the stationary case, the forcing is seen to induce some anisotropy and a spectrum in…

Chaotic Dynamics · Physics 2015-05-28 Benjamin Miquel , Nicolas Mordant

This paper concerns the elastic structures which exhibit non-zero strain at free equilibria. Many growing tissues (leaves, flowers or marine invertebrates) attain complicated configurations during their free growth. Our study departs from…

Mathematical Physics · Physics 2009-07-13 Marta Lewicka , Reza Pakzad

Analytic results for the asymptotic decay of the electron density matrix in insulators have been obtained in all three dimensions ($D=1 - 3$) for a tight-binding model defined on a simple cubic lattice. The anisotropic decay length is shown…

Condensed Matter · Physics 2009-11-07 S. N. Taraskin , D. A. Drabold , S. R. Elliott

We study dispersion properties of layered metal-dielectric media having different layers thicknesses ratios. Plotting dispersion diagrams and isofrequency contours, we find that strong nonlocality is inherent property of such periodic…

Optics · Physics 2012-10-11 Alexey A. Orlov , Ivan V. Iorsh , Pavel A. Belov , Yuri S. Kivshar

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…

Optimization and Control · Mathematics 2021-06-09 José A. Iglesias , Martin Rumpf , Otmar Scherzer